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The Chess Variant Pages

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Nested Chess. A variant hiding another on its diagonals. (15x15, Cells: 141) [All Comments] [Add Comment or Rating]
George Duke wrote on 2009-08-10 UTCExcellent ★★★★★
This is the Sawtooth board, found nowhere else in CVPage surprisingly. The other diamond chesses (Betza'a rectahex etc.) are different and only Gilman's Nested Shogi and couple other Gilmans also have it, if adding the one-square cap on each side. Sawtooth is popular in math problems* and puzzles. One finding: that the outer Bishop binding (including corners) becomes isomorphic with perimetre Rook, based on different board sizes by formula. With n= each integer, by 2n+2 for Rook and 4n+3 for Bishop, there are: n=1, Rook on 4x4 = Bishop on 7x7; n=2, Rook on 6x6 = Bishop on 11x11; n=3, Rook on 8x8 = Bishop on 15x15. Thus Rook on standard 64 squares is oh so like Bishop binding-one on 15x15 Sawtoothed. In Rectahex
Betza uses different diamond geometry, not Sawtooth, to get hexagram connectivity. 
*When referring to recreational math above, remember to try innocently to emulate Einstein in no way diddly doodling, as it turned out, at the Swiss Patent Office by daydreaming in the utmost possible depth for the photoelectric effect and special relativity. Who knows where the chicken scrawls may lead?(war is imbedded in *scrawl*.)
Betza begins: ''Is hexagonal chess really hexagonal, or is it merely a rectangular dream?''